Well, the principal problem is that such a quick endorsement of a wise man doesn't really fit Josephus either.
If you've read Josephus, you'll notice that he's not writing another Book Of Numbers. He's not just listing people. He tells you what stuff happened. JTB for example is mentioned because he's relevant to an event he's writing about, namely some people are blaming a defeat on the king's execution of JTB.
It's also stuff that is somehow historically important, i.e., ends up affecting or involving people at the top or illustrating some custom or aspect, or stuff he witnessed personally and thinks worth mentioning, not a listing of every time every peasant took a dump.
So if Josephus only mentions, basically, "oh yeah, and there was a teacher called Jesus too and he got nailed" (not his exact words) one problem with that is still that it's disconnected from everything, and as Tim mentioned, it doesn't even fit the page it's on. I mean, so what? How is this Jesus guy important or even connected with anything Josephus writes about? What did he DO?
I mean, I can imagine that if he indeed was a famous teacher and he gathered quite the number of disciples, Josephus would have a reason to write about him. But then he'd write about him, not just throw in a one-liner about his mere existence.
The other problem is that if Jesus was famous enough for Josephus to know about him and what he's teaching... I doubt that Josephus would have called him wise or write a gushing endorsement about those learning from Jesus.
Again, Josephus was trying to set up his patron, the new Roman Emperor, as the real messiah that was prophecised by the scriptures. He thinks the Jews were in error when they thought the messiah would come from among them. He spoke rather harshly in fact. This is from
The Wars Of The Jews, Book 6, chapter 5, the last paragraph:
Now if any one consider these things, he will find that God takes care of mankind, and by all ways possible foreshows to our race what is for their preservation; but that men perish by those miseries which they madly and voluntarily bring upon themselves; for the Jews, by demolishing the tower of Antonia, had made their temple four-square, while at the same time they had it written in their sacred oracles, "That then should their city be taken, as well as their holy house, when once their temple should become four-square." But now, what did the most elevate them in undertaking this war, was an ambiguous oracle that was also found in their sacred writings, how," about that time, one from their country should become governor of the habitable earth." The Jews took this prediction to belong to themselves in particular, and many of the wise men were thereby deceived in their determination. Now this oracle certainly denoted the government of Vespasian, who was appointed emperor in Judea. However, it is not possible for men to avoid fate, although they see it beforehand. But these men interpreted some of these signals according to their own pleasure, and some of them they utterly despised, until their madness was demonstrated, both by the taking of their city and their own destruction.
So, you know, those people who thought a messiah would come from among them were "deceived." And "their madness was demonstrated." He's not exactly mourning even their destruction by the Roman armies. Josephus isn't really a fan of those who received that kind of knowledge, to put it mildly.
So, you know, I don't think he'd be exactly gushing about the wisdom of yet another Jewish messiah pretender, or about those receiving it with pleasure